Related papers: Hydrodynamics for quasi-free quantum systems
The relativistic hydrodynamical equations are being examined with the aim of extracting the quantum-mechanical equations (the relativistic Klein-Gordon equation and the Schr\"odinger equation in the non-relativistic limit). In both cases it…
By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a system of quasilinear equations, where stability conditions can be determined by the analysis of its…
In a previous paper, we have developed a general theory of thermodynamic limits. We apply it here to three different Coulomb quantum systems, for which we prove the convergence of the free energy per unit volume. The first system is the…
In this paper we deal with the low Mach number limit for the system of quantum-hydrodynamics, far from the vortex nucleation regime. More precisely, in the framework of a periodic domain and ill-prepared initial data we prove strong…
Shielding effects in non-degenerate and degenerate plasmas are compared. A detailed derivation of the Wigner-Poisson system is provided for electrostatic quantum plasmas where relativistic, spin and collisional effects are not essential.…
Five-moment approximation in hydrodynamics includes not only continuity equation and momentum balance equation, but also energy equation. Set of hydrodynamic equations is presented for system of non-relativistic quantum particles with…
We consider hydrodynamic limits of interacting particles systems with open boundaries, where the exterior parameters change in a time scale slower than the typical relaxation time scale. The limit deterministic profiles evolve…
Second-order relativistic hydrodynamics is surprisingly predictive, even in the presence of large gradients. The hydrodynamic expansion from the method of moments does not require a gradient expansion, but it is intrinsically bound to the…
A hydrodynamic approach is used to calculate an asymptotics of the Emptiness Formation Probability - the probability of a formation of an empty space in the ground state of a quantum one-dimensional many body system. Quantum hydrodynamics…
At its core, hydrodynamics is a many-body low-energy effective theory for the long-wavelength, long-timescale dynamics of conserved charges in systems close to thermodynamic equilibrium. It has a wide range of applications spanning from…
We discuss the transition from a quantum to a classical domain for a model where a separation into environment and system is explicitely not given. Utilizing the coarse graining procedure for free quantum fields we also apply the projection…
We prove quenched hydrodynamic limit under hyperbolic time scaling for bounded attractive particle systems on $\Z$ in random ergodic environment. Our result is a strong law of large numbers, that we illustrate with various examples.
An infinite particle system of independent jumping particles in infinite volume is considered. Their construction is recalled,further properties are derived, the relation with hierarchical equations, Poissonian analysis, and second…
By using the quantum maximum entropy principle we formally derive, from a underlying kinetic description, isothermal (hydrodynamic and diffusive) quantum fluid equations for particles with Fermi-Dirac and Bose-Einstein statistics. A…
In this paper we derive a semiclassical hydrodynamic system for electron densities and currents in the two energy bands of a semiconductor. We use the semiclassical Wigner equation with a k.p Hamiltonian and a BGK dissipative term to…
We study the emergence of gradient flows in Wasserstein distance as high friction limits of an abstract Euler flow generated by an energy functional. We develop a relative energy calculation that connects the Euler flow to the gradient flow…
Obtaining rigorous and general results about the non-equilibrium dynamics of extended many-body systems is a difficult task. In quantum lattice models with short-range interactions, the Lieb-Robinson bound tells us that the spatial extent…
We study a partially ionized hydrogen plasma by means of quantum molecular dynamics, which is based on wave packets. We introduce a new model which distinguishes between free and bound electrons. The free electrons are modelled as Gaussian…
In this paper we study existence of traveling waves for 1-D compressible Euler system with dispersion (which models quantum effects through the Bohm potential) and nonlinear viscosity in the context of quantum hydrodynamic models for…
The hydrodynamic equations for a model of a confined quasi-two-dimensional gas of smooth inelastic hard spheres are derived from the Boltzmann equation for the model, using a generalization of the Chapman-Enskog method. The heat and…